Question: Simplify the following expression: $ z = \dfrac{-5}{2} + \dfrac{-5k + 2}{10} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{10}{10}$ $ \dfrac{-5}{2} \times \dfrac{10}{10} = \dfrac{-50}{20} $ Multiply the second expression by $\dfrac{2}{2}$ $ \dfrac{-5k + 2}{10} \times \dfrac{2}{2} = \dfrac{-10k + 4}{20} $ Therefore $ z = \dfrac{-50}{20} + \dfrac{-10k + 4}{20} $ Now the expressions have the same denominator we can simply add the numerators: $z = \dfrac{-50 - 10k + 4}{20} $ $z = \dfrac{-10k - 46}{20}$ Simplify the expression by dividing the numerator and denominator by 2: $z = \dfrac{-5k - 23}{10}$